이스트 단백질에 대한 단백질-단백질 네트워크의 생물학적 및 물리학적 해석 ; 라플라스 행렬에 대한 고유치 분석과 섭동분석

천무경,장익수,김충락,문은정,유우경 한국물리학회 2007 새물리 Vol.55 No.1

The protein-protein interaction network plays an important role in understanding the various biological functions of proteins. Currently, high-throughput experimental techniques (two-dimensional gel electrophoresis, mass spectroscopy, yeast two-hybrid assay) provide us with a vast amount of data for protein-protein interactions an the proteome scale. If the role of each protein in its network is to be recognized, the efficient bioinformatical and statistical-physics methods are required. We suggest a systematic method that can be used to analyze the protein-protein interaction network and to determine the biological and physical essence of the network$^\prime$s topological character, the stability of the protein-protein network, and the sensitivity of each protein along the biological pathway of its network. We set up the Laplacian matrix of spectral graph theory based on the protein-protein interaction network of yeast proteome and performed an eigenvalue analysis. We applied a perturbation method to the Laplacian matrix, which allowed us to recognize the center of the protein cluster as well as the identity of the hub proteins around the center of the cluster and their relative sensitivities. The results of our systematic analysis agreed well with the experimental findings for the yeast proteome. Our analysis method is robust for understanding and analyzing various kinds of biological, social, and economical networks. 세포 내부에서의 여러가지 생물학적 기능을 이해하는데 단백질-단백질 상호작용의 네트워크가 중요한 역할을 한다. 현재 2차원 전기영동, 질량 분석 및 이스트 단백질 실험 등에 의해 단백질체에 관한 데이터가 대용량으로 생산되고 있다. 이러한 단백질-단백질 네트워크에서 각 단백질의 역할을 이해하기 위해서는 효율적인 생명정보학적 및 통계물리학적인 해석방법이 필요하다. 이 논문에서 우리는 단백질-단백질 상호작용 네트워크를 체계적으로 해석할 수 있고, 그 네트워크의 위상학적인 성질의 생물학적 및 물리학적 기능을 파악하면서 생물학적 경로상에서의 단백질의 민감도를 기술하기 위해 그래프 이론으로부터 유래한 라플라스 행렬 (Laplace matrix)을 사용하여 이스트 단백질의 단백질-단백질 네트워크를 분석하였다. 라플라스 행렬의 고유치문제를 풀고 섭동론적 방법을 적용하여 단백질-단백질 네트워크에서 허브 (hub)의 중심과 각 허브에 있는 단백질 및 그들사이의 상대적 민감도를 분석하였다. 이스트 단백질의 단백질-단백질 네트워크에 대한 우리의 분석결과는 실험적 분석의 결과와 잘 일치하였으며, 우리가 제안한 라플라스 행렬의 방법은 여러가지 다른 네트워크를 분석하는데 유용하게 적용이 되리라 믿는다.

Clustering of The Protein Design Alphabets by Using Hierarchical Self-Organizing Map

천무경,장익수 한국물리학회 2004 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.44 No.6

Twenty kinds of amino acids are building blocks for proteins. The classication of characters of amino acids helps to reduce the complexity of protein properties. Here, we present the classication of 20 amino acids by using hierarchical self-organizing map clustering with the Miyazawa-Jernigan pairwise-contact energy parameters. The classication not only gives the biological interpretations for each group, whose clusterings are in agreement with those of the previous works, but also provides more detailed and characteristic features of amino acid clustering. Hydrophobic, medium, loop-favoring, and polar amino acids are grouped, and each representative amino acid is identied. Hierarchical self-organizing map clustering is proven to be a good clustering tool for classifying the 20 amino acids.

A Self-Organizing Map of Amino Acids with Their Local Environments in Proteins by Using Pairwise-Contact Energy Parameters

천무경,장익수,김충락,Muyoung Heo 한국물리학회 2005 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.47 No.3

Based on the 180 180 pairwise-contact energy parameters between 20 amino acids incorporating their 9 local environments in proteins, the classiation of 180 types of amino acids is presented by the self-organizing map. We demonstrate that the physico-chemical features of the amino acids arewell captured in the 180 180 pairwise-contact energy parameters and that they agree with their known biological characters in the simultaneous aspects of secondary structures, hydrophobicity, and the existence probability of amino acids under various environments in protein structures. Ourresult justis the use of these energy parameters for the recognition of protein folds.

Environment-Dependent One-Body Score Function for Proteins by the Perceptron Learning and the Protein Threading

천무경,장익수,문은정,김해진,정광훈,허무영,김석만 한국물리학회 2004 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.45 No.2

The design and construction of a global protein energy function which can recognize the nativefolds of all representative proteins of dierent classes with a low sequence homology has been oneof the important issues and a formidable task in protein science. We used perceptron learning andprotein threading to construct a one-body score function of proteins, which could recognize simultaneouslythe native folds of 1,006 training proteins covering all available representative proteins ina sequence homology with less than 30 % between them. When the score parameters for the 1,006training proteins were subject to a threading test, 370 (96.9 %) native folds of the 382 new distinctproteins were recognized compared to the previous score parameters obtained using 387 trainingproteins, which recognized 190 (89.2 %) native folds of the 213 new proteins. We performed ananalysis of the score parameters by using a singular value decomposition and a self-organizing mapto elucidate the biological clustering characters of 20 amino acids. The self-organizing map analysisof the new score-parameters revealed better biological clustering of 20 amino acids, which agreedwith their known properties. The same analysis for the previous score-parameters could not providesuch a result because the 387 training proteins employed before did not fully cover all representativeproteins of dierent classes of a sequence homology with less than 30 % between them. We illuminatedthe marked dierence in the new score-parameters that relative to previous score-parameters,not only performed better in recognizing the native folds of new distinct proteins but also capturedbetter the biological clustering characters of amino acids. The design and construction of a global protein energy function which can recognize the native folds of all representative proteins of dierent classes with a low sequence homology has been one of the important issues and a formidable task in protein science. We used perceptron learning and protein threading to construct a one-body score function of proteins, which could recognize simultaneously the native folds of 1,006 training proteins covering all available representative proteins in a sequence homology with less than 30 % between them. When the score parameters for the 1,006 training proteins were subject to a threading test, 370 (96.9 %) native folds of the 382 new distinct proteins were recognized compared to the previous score parameters obtained using 387 training proteins, which recognized 190 (89.2 %) native folds of the 213 new proteins. We performed an analysis of the score parameters by using a singular value decomposition and a self-organizing map to elucidate the biological clustering characters of 20 amino acids. The self-organizing map analysis of the new score-parameters revealed better biological clustering of 20 amino acids, which agreed with their known properties. The same analysis for the previous score-parameters could not provide such a result because the 387 training proteins employed before did not fully cover all representative proteins of dierent classes of a sequence homology with less than 30 % between them. We illuminated the marked dierence in the new score-parameters that relative to previous score-parameters, not only performed better in recognizing the native folds of new distinct proteins but also captured better the biological clustering characters of amino acids.

Double Transitions and Temperature-Independent Coarsening Dynamics of the Coupled XY-Ising Model

장익수,천무경,정광훈,허무영 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.53 No.2

We study the non-equilibrium coarsening dynamics and the short-time dynamics of the coupled XY-Ising model with continuous U(1) and discrete Z2 symmetry, which is believed to be the same universality class of the fully frustrated XY model (FFXY) near phase-transition points. Extensive simulations using heat-bath dynamics with U(1) variables show that the critical behaviors of this model agree with the recent suggestions for the FFXY model having double transitions and a non- pure Ising exponent, but a careful analysis also demonstrates that the domain growth laws below the critical temperature do not follow the temperature-dependent growth law of the FFXY model; rather, they follow the temperature-independent ordering kinetics, at least above T ≥ 0.1J/kB, of the pure XY and the pure Ising models.

싸이트 스며들기 클러스터의 다항 분열 축척 현상

허무영,천무경,장익수 한국물리학회 2009 새물리 Vol.59 No.2

Multiple fragmentation behavior appears in various random systems, such as porous media, coal particles, branched polymers, etc. whose structures can be modeled by using a site percolating cluster. The important quantities to describe such fragmenting behavior are the fragmentation rate and the mass distribution of fragmented objects in a random system. We generate the site percolating cluster by using the Leath algorithm and calculate the average number of fragmentating sites and the mass distribution of fragmented site percolation clusters by using the burning algorithm. We checked whether these two quantities in multiple fragmentation follow the scaling behavior of binary fragmentation, Edward's scaling law of binary fragmentation, and showed that a universal scaling behavior exists for both binary and multiple fragmentations. 다항 분열 현상은 본드 스며들기 클러스터에서 뿐만아니라 싸이트 스며들기 클러스터에서도 공통적으로 일어나는 현상이다. 리스 알고리듬(Leath Algorithm)을 이용하여 싸이트 스며들기 클러스터를 생성시킨 후, 분열 싸이트의 평균 개수(as)와 이것의 크기 분포(bs's)를 버닝 알고리듬(burning algorithm)을 이용하여 계산하였다. 우리는 다항 분열 현상에서의 as와 bs's가, 이항 분열(binary fragmentation)에서 성립하는, Edward의 축척 법칙(scaling law)을 따르는가를 검증하였으며, 이 결과로부터 싸이트 스며들기 클러스터의 이항 분열 현상과 다항 분열 현상 사이에는 공통적으로 만족되는 보편적인 축척 법칙이 존재함을 보였다.

Significant improvement of the pairwise contact energies for proteins

허무영,장익수,Eun-Joung Moon,정광훈,천무경,김석만 한국물리학회 2004 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.44 No.6

Recent attempts to construct a global pairwise contact energy function of amino acids for proteins have not succeeded in stabilizing the native states of many proteins simultaneously. In this paper, we show that the systematic inclusion of the local environments of the amino acids in the design of such a function leads to success in designing a global protein energy function. We design and construct two kinds of pairwise contact energy functions by considering either the secondary structures or the hydrophobicities (solvation) of the amino acids and by using perceptron learning and protein threading. These can stabilize all native states of 1,006 proteins simultaneously with 30 % homology. When these two energy functions are subject to a threading test on 382 new distinct proteins, the energy function with the secondary structure information can stabilize 300 (78.5 %) proteins out of 382 proteins whereas the energy function with the hydrophobicity information can stabilize 367 (96 %) proteins. This illustrates the critical role played by the hydrophobicity of amino acids in stabilizing the essential structures of proteins. Both the hydrophobicity and the secondary structure are important to assess the protein structure, and the impact of the hydrophobicity is elucidated in this work through the process of designing global pairwise contact energies for proteins. We expect that the simultaneous inclusion of the hydrophobicity, the secondary structure, and other local environments, such as the polarity and the structures of neighboring of amino acids, will enable us to design better protein energy functions by using perceptron learning and protein threading. .Recent attempts to construct a global pairwise contact energy function of amino acids for proteins have not succeeded in stabilizing the native states of many proteins simultaneously. In this paper, we show that the systematic inclusion of the local environments of the amino acids in the design of such a function leads to success in designing a global protein energy function. We design and construct two kinds of pairwise contact energy functions by considering either the secondary structures or the hydrophobicities (solvation) of the amino acids and by using perceptron learning and protein threading. These can stabilize all native states of 1,006 proteins simultaneously with 30 % homology. When these two energy functions are subject to a threading test on 382 new distinct proteins, the energy function with the secondary structure information can stabilize 300 (78.5 %) proteins out of 382 proteins whereas the energy function with the hydrophobicity information can stabilize 367 (96 %) proteins. This illustrates the critical role played by the hydrophobicity of amino acids in stabilizing the essential structures of proteins. Both the hydrophobicity and the secondary structure are important to assess the protein structure, and the impact of the hydrophobicity is elucidated in this work through the process of designing global pairwise contact energies for proteins. We expect that the simultaneous inclusion of the hydrophobicity, the secondary structure, and other local environments, such as the polarity and the structures of neighboring of amino acids, will enable us to design better protein energy functions by using perceptron learning and protein threading.

Development of a Thermodynamic Approach to Clustering Ensemble Structures for a Native State of a Protein from NMR Experiment: Application to a Cancer Suppressor Protein P53

김석만,장익수,문은정,Haejin Kim,정광훈,천무경,허무영,이원태 한국물리학회 2004 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.45 No.2

..NMR experiments for resolving protein structures provide ensemble structures that have dierent features from the unique ones obtained from X-ray crystallography experiments. Currently, the conventional methods to select good structures for a native state from NMR rely on choosing structures with geometrical similarity, for example root-mean-square deviation(RMSD), in the ensemble of protein structures. However, the conventional approach can clarify nothing but a geometrical convergence of ensemble structures, with which one assumes that the structures of low energies and with smaller RMSD values are candidates for a native-state structure of a target protein. Here, we suggest a statistical physics approach to probe the thermodynamic stability of ensemble structures resolved in NMR experiment and to identify a set of ensemble structures possessing thermodynamic equivalence as candidates for a native-state structure. We employed a coarse-grained description for a global protein energy function based on the environmental energy parameters of 20 amino acids, which were constructed by perceptron learning and protein threading of 1,006 representative proteins. We constructed an approximate partition function in the conformational space of decoy conformations, although it was not albeit exact. We calculated the unfolded fraction and the speci c heat of the tetramerization domain of an important cancer suppressor protein p53 as a function of temperature. Applying our approach to the 20 (78) ensemble structures of the 1HS5 (1SAK) group, 9 (72) out of 20 (78) ensemble structures were interpreted as thermodynamically equivalent and could be considered as a good set of native-state structures with relatively high thermodynamic stabilities whereas the remaining 11 (6) ensemble structures should have been removed from the candidate structures for a native state in the NMR experiment. After rening the ensemble structures of 1SAK to have 3SAK experimentally, the 23 new ensemble structures of 3SAK showed a good thermodynamic equivalence in their unfolded fraction and specic heat curves. Our statistical physics approach is a new alternative method for characterizing the thermodynamic behavior of ensemble structures of a target protein in NMR experiments and to select a good set of ensemble structures for a native state. If our approach is combined with the conventional geometrical method, it will greatly facilitate the identication and characterization of ensemble structures of a target protein in NMR experiments. .NMR experiments for resolving protein structures provide ensemble structures that have dierent features from the unique ones obtained from X-ray crystallography experiments. Currently, the conventional methods to select good structures for a native state from NMR rely on choosing structures with geometrical similarity, for example root-mean-square deviation(RMSD), in the ensemble of protein structures. However, the conventional approach can clarify nothing but a geometrical convergence of ensemble structures, with which one assumes that the structures of low energies and with smaller RMSD values are candidates for a native-state structure of a target protein. Here, we suggest a statistical physics approach to probe the thermodynamic stability of ensemble structures resolved in NMR experiment and to identify a set of ensemble structures possessing thermodynamic equivalence as candidates for a native-state structure. We employed a coarse-grained description for a global protein energy function based on the environmental energy parameters of 20 amino acids, which were constructed by perceptron learning and protein threading of 1,006 representative proteins. We constructed an approximate partition function in the conformational space of decoy conformations, although it was not albeit exact. We calculated the unfolded fraction and the speci c heat of the tetramerization domain of an important cancer suppressor protein p53 as a function of temperature. Applying our approach to the 20 (78) ensemble structures of the 1HS5 (1SAK) group, 9 (72) out of 20 (78) ensemble structures were interpreted as thermodynamically equivalent and could be considered as a good set of native-state structures with relatively high thermodynamic stabilities whereas the remaining 11 (6) ensemble structures should have been removed from the candidate structures for a native state in the NMR experiment. After rening the ensemble structures of 1SAK to have 3SAK experimentally, the 23 new ensemble structures of 3SAK showed a good thermodynamic equivalence in their unfolded fraction and specic heat curves. Our statistical physics approach is a new alternative method for characterizing the thermodynamic behavior of ensemble structures of a target protein in NMR experiments and to select a good set of ensemble structures for a native state. If our approach is combined with the conventional geometrical method, it will greatly facilitate the identication and characterization of ensemble structures of a target protein in NMR experiments.

단백질 자연구조의 인식에 있어서 라마찬드란 각의 역할 및 기여도

허무영,장익수,김석만,문은정,정광훈,천무경 한국물리학회 2004 새물리 Vol.48 No.3

. In order to recognize better native folds of proteins, we improved the old environmental parameters of amino acids and set up new environmental parameters. Usually, the feature of protein structures is extracted by using environmental parameters which include the protein's secondary structure and the burial degree of amino acids in a protein's structure. In this research, we investigated the important role of the Ramachandran angles in the environmental parameters. For the each cases of energy (score) functions without and with Ramachandran angles and using a statistical method, the success ratios for recognizing the proteins' native structures were respectively, 62.4 % and 77.3 %. Combining Ramachandran angles with the old environmental parameters of the protein energy function improves it's capability to recognize the native structures of proteins by 14.9 %. An effort to achieve complete recognition of all native folds of 1,006 proteins is now being undertaken by using perceptron learning and protein threading.